Heart valve surgery can be used to repair or replace diseased heart valves. For example, heart valve replacement may be indicated when there is a narrowing of the native heart valve, commonly referred to as stenosis, or when the native valve leaks or regurgitates. The repair or replacement of diseased heart valves can include, for example, the introduction of a prosthetic heart valve that includes biological tissue heterologous to the patient (e.g., a heterograft or xenograft). Pericardial tissue from the sacs surrounding the hearts of animals, e.g. bovine, porcine, and equine, etc., are commonly used to create tissues that can be used in various medical applications. Biological tissue can have mechanical properties that vary within a single donor and/or from among several donors of the same species. For example, biological tissue from a single donor can have non-uniform thickness and/or stiffness, and the average thickness and/or stiffness of biological tissue can vary from one donor to another. The variation in mechanical properties of biological tissue used in replacement heart valves can impact the performance and/or durability of a replacement heart valve implanted in a patient. In some cases, the pericardial sacs can be cut, treated, and selected to obtain desirable mechanical properties, but these treatment and selection processes can result in significant quantities of unused pericardial tissue. Accordingly, there is a need improved techniques for treating and cutting pericardial tissue to obtain desirable properties while minimizing waste.